SpikeTV's "MANswers" show once did a feature where they asked if you could kill someone by shooting a gun high into the air, and having the bullet come back down and kill someone. They said the answer was no; when the bullet is coming down it will be too slow due to its light weight and air resistance, and no longer lethal.

But what about if you shoot a gun upward at an angle, such as 45 degrees, etc? When the bullet comes back down, which will probably be a LONG distance away, will it still be lethal? This knowledge might be helpful when considering what happens when you miss your target and may hit an innocent bystander. In some situations, perhaps you could have the option of angling your shot upwards enough so that even if you miss, you will be safe to bystanders behind the target, because in order for them to be hit the shot has to be coming back down, and by that time the bullet would have to be so far away and so slowed down that it may no longer be lethal.

32.4 degrees...











Actually I pulled that number outta my butt.  As a general rule, bullets should never be considered "safe" if fired at or in the direction of others. Regardless of whatever they show on TV. There are just too many variables (bullet mass, muzzle velocity, altitude, temperature, etc), to say with absolute certainty that no deadly harm would result.

I don't think it's aerodynamic enough in the bullet's design to maintain the airpocket or lift or whatever it's called once the kinetic energy disipates behind the actual bullet. I think the rule of terminal velocity takes effect once the only form of propulsion is depleted. So the bullet itself, as light as it is, is going to be subject to the forces of gravity. In other words, it's still falling toward the earth in the weight vs air resistance formula.

But that's just my GED attempt at explaining it. lol. I'm sure there's someone smarter around here.

Bullets are not safe on the receiving end.

That is why people use firearms for hunting and self defense.

Know your target and what is beyond.  You are still liable for your projectile, no matter what angle you fire your weapon.  You have to mitigate the risks if the need arises to shoot.

That's right, those middle eastern guys are always shooting their 7.62x39's straight up to the sky! Maybe the turbans brake the impact..

I didn't study most of the time during physics in college, but Mythbusters the show did a study abou this topic.  They found that if you shoot  a bullet straight up in the air, it didn't have enough force to kill someone.  They actually shot a handgun 90degrees into the air and found the projectile in the desert and measured the force by how deep it embeded into the ground.  Interesting if there was an angle involved and I would dare to say that it would be lethal and there would still be a lot of force still pushing the bullet other than gravity, otherwise it would just fall straight down.

I remember hearing gun shots all night on New Years Eve while growing up in Ewa..and a lot more at midnight...

I remember hearing gun shots all night on New Years Eve while growing up in Ewa..and a lot more at midnight...

Yep, I remeber that also, but back then there were cane fields all around.   

Not much shootin anymore, but I still heard some shots.  Hope they were pointing that stuff towards the ocean!

Hmm, maybe it was Mythbusters and not MANswers that did this feature, I can't remember.

Reading the article that Funtimes linked, I would agree that even a bullet shot straight up into the air could potentially hurt someone. But it is on the borderline. I think the chances are low enough that it's useful to know. Even if someone is unlucky enough to be hit by a falling bullet, they still have a good chance of being relatively uninjured. Essentially they would have to be unlucky two times in a row to suffer a major wound.

But here is where things get interesting. It's wrong to assume that if straight up is borderline safe/unsafe, that 45 degrees would be much worse. I would be willing to bet a lot of money that 70 degrees up yields the exact same result as 90 degrees up. Either way, the bullet should reach terminal velocity before coming back down. I wouldn't be surprised if 45 degrees is also the same result as 90 degrees. Unfortunately this is hard to predict or calculate; maybe the best way to solve this question is via direct experimentation, so hopefully Mythbusters or MANswers would be willing to do a follow up feature...Now where are those forums for submitting questions to them...

I have a masters degree in physics from long ago, so I guess I like to do this sort of thinking.

edit: On second thought, although it would be hard to calculate the answer (as opposed to experimenting to find it), it is far from impossible. If I feel like it maybe I'll try.

My answer is "it depends."  You can shoot a 16" shell at 90 degrees and I guarantee you it will kill someone when it comes back down and squishes a person.

These questions can be affirmatively answered in Hatcher's Notebook in his chapters on "How far will my gun shoot?" and "Bullets from the sky."

Distance versus elevation, and lethality, are pretty much determined by the weight of the projectile in our "sea of air."

For heavier projectiles, air resistance becomes less and less of a factor in the trajectory, but they are more and more lethal.  This sample passsage will answer some questions:

Years ago our seacoast defenses included heavy mortar batteries and the big, low-velocity shells required an elevation of 45° to attain maximum range. (snip) The 12" coast-defense mortar shell, weighing 824 lbs, gave a maximum range of about 12,000 yards when fired with a muzzle velocity of nearly 1300 feet per second... this is about 71% of its vacuum range.

Something over half a century ago I happened to have command of a battery of 12-inch mortars in the coast defenses of Pensacola, FL, and I knew from first hand experience that there was no mystery about where the shells would come down, such as there is with small arms bullets.  The weight of the shell, and its enormously greater ballistic coefficient make all the difference.  With our fire control instruments and our range tables, we knew exactly where the shells would fall, and could fire these guns with great accuracy at moving targets distance 10,000 yards or more.  The very long time of flight, 30 seconds or more, had to be allowed for, but we had instruments to do it, and the results were good.

You will notice that with lighter projectiles, the angle of departure for maximum range is much less than the 45° usually quoted for a maximum range.

I abstract some of his comment here (not really a direct quote):

A 174 gr bullet at 2600 fs (similar to the cal .30-06) will attain its maximum range of about 4400 yards when fired at an elevation between 29° and 35°.  A cal .45 ACP bullet at around 820 feet per second, weighing 230 gr, will attain a maximum range of about 1600 yards, probably at something like 35° elevation.

For comparison, the ultimate vacuum range of a .30-06 at 2700 feet per second, would be about 43 miles if fired at the 45° angle.

Hatcher describes many experiments with vertical firing of small arms --turns out it's pretty difficult to get a little tiny bullet, what with the strong winds aloft, to land anywhere near where it is fired from.

He goes on to mention that the service cartridge bullet (.30-06), when fired vertically, will have about 300 ft per second of terminal velocity, enough to cause a disabling wound, but not necessarily lethal.  Amusingly, they had a lot of difficulty in getting the bullets to land nearby, and had to use a vertically-mounted machine gun infull-auto to figure out where the bullets were landing so that adjustments could be made to bring the impact points close to the observation platform.

With some particular bullets, about half of them turned over in flight so they came down point first --the others landed base first, one leaving a slight dent in the wood observation boat.

I strongly advise that anyone with a serious interest in firearms obtain a copy of this book.  I would bet about 85% or more of questions posed on gun forums can be answered from this book.  Some of the information is fairly dated, in terms of the arms and ammunition available in his time, but the physics are not dated.

The general answer to firing celebrity shots into the air is that firing vertically, the bullets coming down are not as dangerous since there is no horizontal velocity, and the terminal velocity in coming down is pretty low.  In firing them at lower angles, however, the horizontal velocity remains high, thus making the bullets far more dangerous.

However, neither of these practices are safe, and are not to be recommended unless there is a large empty area where the projectiles will land... such as over the empty ocean, or on the Pawnee National Grasslands, where I used to shoot 12-gauge slugs along the ground just to watch them make puffs of dust with each bounce.  (This was perfectly safe in that area at that time.)

One interesting fact that emerged from the Ordnance Department experiments was that at normal velocities for a given cartridge, increasing the muzzle velocity makes only a minor difference in the range that can be attained.

Example:  Two cartridges are loaded, cartridge A to 2600 feet per second, cartridge B to 2700 feet per second, a difference of 100 feet per second.

The difference in ranges will be equaivalent to the distance it takes for the bullet from B to slow down to the muzzle velocity of A.

If bullet B will slow down 100 feet per second in its first 100 yards of travel, then its ultimate range will be only 100 yards greater than the range of bullet B.


Terry, 230RN

Terry,
I believe that is the best, most complete, answer to a forum question I have ever seen to date!
Thank you very much!

Well there you go, don't shoot your gun up in the air.  It may be less lethal, but why take that chance!

I need to study more on my longrange ballistics!

Actually, although everything just discussed by 230RN was true, it did not answer the question I have posed as the thread topic.

If you want to be picky about semantics, I can just remove the word "safe" from the topic title and replace it with "generally nonlethal". I know that it is not a good idea to assume that things are ever safe. But that doesn't have to prevent us from asking the question.

And if you want to be picky about caliber, I could just specify 9mm Parabellum, which will be much less lethal in this scenario (extreme long distance ballistics) than a .30-06 rifle cartridge.

Actually, although everything just discussed by 230RN was true, it did not answer the question I have posed as the thread topic.

That's funny.

Heres my answer...
Trajectory tolls the holding brick. The deaf executes the mob rage under a clinic. The lover transports the oriental risk. Bullet loses inside the static. This lost material lumps the trail. Why can't Trajectory participate before Bullet?
The eating starter volunteers near a doubling horizon. A risk rests against the mint. Will the feeling appeal train Bullet? Bullet detaches a spiritual exposure around the winning motorway. A gathering profile socks Trajectory.
Bullet invokes an attendant west. The profit skips! A shallow instinct defines Bullet. How will Trajectory exit? A transformed faith orbits before the story.
A wound atom hails the hacking law. Does Bullet dress? The expert owner chews Bullet. Does the fewer food study throughout Bullet? The socialist rates Bullet.
Trajectory mutters next to the medium luck. Should the punished innocence pass Bullet? Does Bullet hurt Trajectory? An activating ocean kisses the mechanic boat. The flat vowel tones his greedy journalist.

Thanks for the additional information regarding the specific caliber of interest.

I do not consider any strike from a fired bullet as "generally safe" or "generally nonlethal" and will not speculate on the definitions of those terms. One can possibly drop an elephant in its tracks with a .177 pellet gun if you hit him in the eyeball.

I can only give the facts.

Page 547, Hatcher's Notebook, Table 4, lists the extreme range of the 9mm (assuming a sharp point on a 124 grain bullet with a muzzle velocity of 1140 feet per second) as 1900 yards, 1.08 miles.  Departure angle in this instance is not given, but an educated guess would be 30°  to 35°, if you could even measure it that closely in the field. However, it should be obvious that any angle different from that which gives the extreme range will result in a shorter range.  Thus, the "safety zone," if you will, will be outside of 1900 yards regardless of the angle at which the gun is fired.  This, assuming the projectile actually stops when it intersects the surface of the earth.

Table 4 also gives extreme ranges for a number of other cartridges from .22WRF to .458 Winchester one may find of interest.

Table 5 gives similar information for shotgun pellets.

I'm pretty sure I understand what you are asking, but there is no definitive answer to your question as posed, since the weight of the bullet and the height it fell, as well as whatever ballistic coefficient it presents to the air on the way down are all indeterminate factors. 

Let's also bear in mind that its remaining horizontal velocity component becomes more important in wounding power as the firing angle is decreased. Or, to turn it around to match your question, the wounding power decreases as the firing angle is increased.

But all this is just as indeterminate without further specification of the problem and also depends on the definition of "lethality" or wounding power.  Tossing a 124 grain bullet from one hand to the other is not very hurtful, but catching one at 300 feet per second horizontal component would be dicey.

And dicier still, if it hit you in the temple.

I imagine vertical and horizontal velocity components (and the resultant vectored velocity) for all firing angles could be calculated for any missile whose ballistic properties are very well known, and presuming a firm definition of "lethality" existed.  With all that persnickety information firmed up, and with relative velocities and energies available, a definitive answer might be obtained for, say, one's 124-grain 9mm bullet. 

So the only answer that can be reasonably given with any assurance without this high level of computation (and only  for a specific missile) is the "maximum range" rather than the "highest angle" you could shoot a bullet of any reasonable weight without danger of "seriously" hurting someone if it hit them.

Terry, 230RN

I do not consider any strike from a fired bullet as "generally safe" or "generally nonlethal" and will not speculate on the definitions of those terms. One can possibly drop an elephant in its tracks with a .177 pellet gun if you hit him in the eyeball.

Okay, let's rephrase the question one more time. Replace lethality by final impact velocity. I only wish to know the final impact velocity of a 9mm Parabellum bullet that is fired into the air at a specified angle. If need be we can specify the precise manufacturer make of the 9mm cartridge, but pretty much choose one you like, which you did.

lists the extreme range of the 9mm (assuming a sharp point on a 124 grain bullet with a muzzle velocity of 1140 feet per second) as 1900 yards, 1.08 miles.  Departure angle in this instance is not given, but an educated guess would be 30°  to 35°...However, it should be obvious that any angle different from that which gives the extreme range will result in a shorter range.  Thus, the "safety zone," if you will, will be outside of 1900 yards regardless of the angle at which the gun is fired.

All sounds pretty reasonable. Thanks for the figures.

I imagine vertical and horizontal velocity components (and the resultant vectored velocity) for all firing angles could be calculated for any missile whose ballistic properties are very well known... With all that persnickety information firmed up, and with relative velocities and energies available, a definitive answer might be obtained for, say, one's 124-grain 9mm bullet.

This is the computation or experimental result that I am looking for.

The good news is that we have now formulated the question to be answerable, albeit by complex mathematical procedures.

The bad news is that I don't have those complex mathematical procedures.  Or the time to analyze it more closely than this:

CASE 1:

The bullet is fired from an absolutely horizontal barrel from the shoulder height of a standing man, say five feet.  This bullet will maintain its full "lethality," (or your specified velocity and energy necessary to "not kill") until it drops that five feet and hits the ground. (This conception neglects ricochet danger, if any, after its initial impact with the ground.)  All parameters such as remaining velocity and energy and bullet drop in this CASE 1 are readily determined by conventional ballistic programs, which are ultimately based on empirical measurements taken from test firings and converted to the conventional ballistics tables, e.g., Ingall's Tables.  These tables take into account form factor, ballistic coefficient, and other relevant variables.

CASE 2: 

The  bullet is fired from an absolutely vertical barrel and travels upward to a point where its energy is exhausted by friction with the air and by overcoming the acceleration of gravity.  It then falls back down, regaining velocity until air resistance equals the bullet's weight.  It strikes the ground with this "terminal velocity.  Its "lethality," or, again, your specified velocity and energy necessary to "not kill" can be determined, once again, by empirical experiment.  In the ideal case, where the bullet maintains its point-upward orientation throughout its travel, this can once again be calculated by use of conventional tables, or determined empirically.  In the not-so-ideal case, where the bullet either tumbles or turns over in flight,  there are probably no tables to determine this terminal velocity or energy.

CASE 3:

The bullet is fired at the angle of departure which gives its maximum range, that is, where its trajectory crosses the "five feet" mentioned above, and then falls the additional "five feet" while continuing its trajectory and then hits the ground.  The velocity and energy  can be calculated all along the bullet's path using conventional computational methods to determine where the bullet dops to your your specified velocity and energy necessary to "not kill."

CASE 4 (in brevis):

The bullet is fired at increasing angles to approach CASE 2, the completely vertical.  At some point along this continuum, the horizontal velocity may become low enough that this component of the horizontal energy, combined with the vertical component of the bullet's energy may fall below your specified velocity and energy necessary to "not kill."  One complicating factor in this CASE 4 is the fact that in some cases, since the trajectory of missiles in the air are not exact parabolas (more exactly, segments of an ellipse), the last part of its trajectory may be completely vertical, even though the bullet left the muzzle at a non-vertical angle.  Even an inert mortar shell, falling almost vertically, will be deadly.  Among other complications.

So the ultimate solution to this CASE 4 is left to the ultimate student, and there is no answer in the back of the book.

It should also be noted that bullet weight is a large factor in these considerations.  After all, a ton-and-a-half 16" shell sitting on your chest, with no energy and no trajectory, will kill you.

Sorry, but as stated, with the complexity involved in your question, even though we have finally clarified its intent, the only reasonable answer without complex math and empirical data, defaults, as stated, to the ultimate range of any given cartridge.  For the 9mm cartridge, this is 1900 yards. For the 124 grain bullet.  At 1140 feet per second. With a sharp nose.

I am sure you are going to press further on the "9mm" question, forgetting that a complete answer will be of no practical benefit except for that particular projectile.

But my work here is done, in terms of hopefully clarifying the general question.  Others may have significant contributions to this thread and I cheerfully admit to copping out on CASE 4.

For I am not the "ultimate student" you are seeking.

I believe, thus far, Colt808 had the best answer:

32.4 degrees...


Actually I pulled that number outta my butt.  As a general rule, bullets should never be considered "safe" if fired at or in the direction of others. Regardless of whatever they show on TV. There are just too many variables (bullet mass, muzzle velocity, altitude, temperature, etc), to say with absolute certainty that no deadly harm would result.

Terry, 230RN